How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which not two S are adjacent ?

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is-

A mass of $100 blank g$ strikes the wall with speed $5 blank m divided by s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2 cross times 10 to the power of negative 3 end exponent s e c$ , what is the force applied on the mass by the wall

If the locus of the mid points of the chords of the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator y to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction equals 1$ , drawn parallel to $y equals m subscript 1 end subscript x$ is $y equals m subscript 2 end subscript x$ then $m subscript 1 end subscript m subscript 2 end subscript equals$

If ⁿC_r denotes the number of combinations of n things taken r at a time, then the expression ⁿC_r+1 + ⁿC_{r –1} + 2 × ⁿC_r equals-

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is $C presuperscript n plus 2 end presuperscript subscript r plus 1 end subscript$ .

If ⁿC_r denotes the number of combinations of n things taken r at a time, then the expression ⁿC_r+1 + ⁿC_{r –1} + 2 × ⁿC_r equals-

The different ways in which items from a set may be chosen, usually without replacement, to construct subsets, are called permutations and combinations. When the order of the selection is a consideration, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination. So the final answer is $C presuperscript n plus 2 end presuperscript subscript r plus 1 end subscript$ .

The number of ways is which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question is -

An intense stream of water of cross-sectional area $A$ strikes a wall at an angle $theta$ with the normal to the wall and returns back elastically. If the density of water is $rho$ and its velocity is $v$ ,then the force exerted in the wall will be

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line $O A$ will

Two small particles of equal masses start moving in opposite directions from a point $A$ in a horizontal circular orbit. Their tangential velocities are $v$ and $2 v$ , respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at $A$ , these two particles will again reach the point $A$

In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is

The number of non-negative integral solutions of x + y + z  n, where n  N is -

Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -

If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -

The number of numbers between 1 and 10¹⁰ which contain the digit 1 is -

The number of rectangles in the adjoining figure is –